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arXiv · 2210.05826

Moduli of curves on toric varieties and their stable cohomology

Oishee Banerjee
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Abstract

We prove that the cohomology of the moduli space of morphisms of a fixed finite degree from a smooth projective curve $C$ of genus $g$ to a complete simplicial toric variety $\mathbb{P}(\Sigma)$, denoted by the rational polyhedral fan $\Sigma$, stabilizes. As an arithmetic consequence we obtain a resolution of the Batyrev-Manin conjecture for toric varieties over global function fields in all but finitely many characteristics.

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Oishee Banerjee. 2022-10-11. Moduli of curves on toric varieties and their stable cohomology. https://arxiv.org/abs/2210.05826

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